Geometric Progression Example

                                            Geometric Progression Example.

Q: In a GP,the third term is 24 and the 6^th Term is 192. Find the 10^th  term?

                                                                  Solution:

We know that the nth  term of an GP is given by:

                                   (a*r^(n-1)).      ….. (1)   

Now, as per the question,the third term is 24,therefore,

                                          24 = a*r^(3-1)      …(2)

And the 6^th term is 192,therefore,

• 192 = a*r^(5-1) …(3)

Therefore,

                             a* r^(5-1) / a*r^(3-1) = 192/24

• r^3 = 8 ==>  r = 2

Thus,we have the common ratio as 2. Now, we will find the first term i.e. a.

Substituting r = 2 in …(2), we have, 4a = 24 (because r^2 = 4) from which a = 6.

Now, we have both the first term as well as the common ratio. Therefore, now to get the 10^th term we simply substitute the values of a and r in a*r^(10-1)and obtain

                                            6*(2^9) which comes out to be 3072.

Thus, we have, as the 10^th term,3072.